A planet has half the mass of the Earth and half the radius. Compared to its weight on Earth, an apple on this planet would weigh _____. A. twice as much B. one-fourth as much C. half as much D. the same E. zero

It depends a little on what it's mainly comprised of. For example, a planet of Tungsten would be twice as dense as the same planet made of Lead. however, given that this is just a hypothetical question, the answer is C.

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hamzaahmeds hamzaahmeds · Answer 2 · 2021-10-21T11:29:01+02:00

This question involves the concepts of acceleration due to gravity, weight, gravitational force, and Newton's gravitational law.

Compared to its weight on Earth, an apple on this planet would weigh "A. twice as much".

First, we will calculate the acceleration due to gravity on the other planet, by equating the weight and the gravitational force on the apple.

First, equating the values on Earth:

[tex]Gravitataional\ Force=Weight\\\\\frac{GmM}{r^2}=mg\\\\\frac{GM}{r^2} = g\\\\g = \frac{GM}{r^2}[/tex]---------- eqn (1)

where,

g = acceleration due to gravity on earth

G = Universal gravitational constant

M = Mass of Earth

r = radius of Earth

Now, writing the sam equation for the other planet:

[tex]g' = \frac{GM'}{r'^2}[/tex]

where,

g = acceleration due to gravity on the other planet

M = Mass of the other planet

r = radius of the other planet

Therefore,

[tex]g' = \frac{G(0.5\ M)}{(0.5r)^2}\\\\g' = 2\frac{GM}{r^2}\\\\using\ eqn\ (1):\\\\g' = 2g ------- eqn(2)[/tex]

Now, we compare weights on both planets:

[tex]W' = Weight\ on\ other\ planet = mg' = m(2g)\\W' = 2mg\\where,\\\\ mg = W = Weight\ on\ Earth\\\\Therefore,\\\\[/tex]

W' = 2W

Learn more about Newton's Law of Gravitation here:

brainly.com/question/17931361?referrer=searchResults

The attached picture illustrates Newton's Law of Gravitation.